If you were caught without dog tags then most would lie or hide that they were Jewish. If you were a known jew then you would be treated much worse but for the most part not killed mostly beaten. However there is one large exception the Berga Camp Incident. It was near the end of the war and a group of POWs were split into Jewish and none Jewish groups. The Jews were sent to a coal mine that functioned as a concentration camp. Of the 350 sent there 27% were dead within 10 weeks by far the highest attrition rate of Western POWs. This incident was very obscure for a long time until around 10 years ago when the New York Times published an article as seen below. There are a few other sources that deal with this topic. One of the better ones would be Men of Honour American GIs in the Jewish Holocaust.

http://www.nytimes.com/2005/02/27/magazine/27PRISON.html?pagewanted=1&_r=0